t numbers after the fourth one? Are there infinitely long arithmetic progressions of consecutive primes? e.g. 251, 257, 263, 269 has length 4. The largest example known has length 10. Are there infinitely many sets of 3 consecutive primes in arithmetic progression. (True if we omit the word consecutive.) n2 - n + 41 is prime for 0 n 40. Are there infinitely many primes of this form? The same question applies to n2 - 79 n + 1601 which is prime for 0 n 79. Are there infinitely many primes of the form n# + 1? (where n# is the product of all primes n.) Are there infinitely many primes of the form n# - 1? Are there infinitely many primes of the form n! + 1? Are there infinitely many primes of the form n! - 1? If p is a prime, is 2p - 1 always square free? i.e. not divisible by the square of a prime. Does the Fibonacci sequence contain an infinite number of primes?Here are the latest prime records that we know. The largest known prime (found by GIMPS [Great Internet Mersenne Prime Search] in December 2001) is the 39th Mersenne prime: M13466917 which has 4053946 decimal digits. The largest known twin primes are 242206083 238880 1. They have 11713 digits and were announced by Indlekofer and Ja'rai in November, 1995. The largest known factorial prime (prime of the form n! 1) is 3610! - 1. It is a number of 11277 digits and was announced by Caldwell in 1993. The largest known primorial prime (prime of the form n# 1 where n# is the product of all primes n) is 24029# + 1. It is a number of 10387 digits and was announced by Caldwell in 1993. ...
